ABSTRACT
In Chapter 7, we have considered randomized phase II trials for comparing the efficacy of an experimental therapy (arm x) with that of a prospective control (arm y) in terms of a binary endpoint, such as tumor response, using a two-sample binomial test. Let px and py denote the true response rates for arms x and y, respectively. We want to test whether the experimental arm has a higher response rate than the control or not, that is, H0 : px ≤ py against Ha : px > py. The null distribution of the binomial test that was discussed in Chapter 7 depends on the common response probability px = py(= p0). Consequently, if the true response probabilities are different from the specified ones, the testing based on binomial distributions may not maintain the type I error rate close to the specified value. In order to avoid this issue, we have considered controlling the type I error rate over the whole range of px = py values, that is, [0, 1]. This conservative control of the type I error rate is equivalent to controlling the type I error rate at px = py = 1/2. This results in an overly strong conservativeness when the true response probability is very different from 50%.
